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Block-adaptive Cross Approximation of Discrete Integral Operators

Title data

Bauer, Maximilian ; Bebendorf, Mario:
Block-adaptive Cross Approximation of Discrete Integral Operators.
In: Computational Methods in Applied Mathematics. Vol. 21 (2021) Issue 1 . - pp. 13-29.
ISSN 1609-4840
DOI: https://doi.org/10.1515/cmam-2019-0085

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Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical matrix approximations having the same prescribed accuracy on all blocks of the partition, for the solution of linear systems it may be more efficient to adapt the accuracy of each block to the actual error of the solution as some blocks may be more important for the solution error than others. To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the block-wise Matrix approximation. This allows to interlace the assembling of the coefficient Matrix with the iterative solution.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: ACA; error estimators; BEM; non-local operators; hierarchical matrices; fast solvers
Subject classification: 65N38
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing > Chair Scientific Computing - Univ.-Prof. Dr. Mario Bebendorf
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Research Institutions
Research Institutions > Research Centres
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 08 Jun 2019 21:00
Last Modified: 31 Jan 2022 07:07
URI: https://eref.uni-bayreuth.de/id/eprint/49454